A combination of spectral and finite elements for an exterior problem in the plane

Applied Numerical Mathematics

Volumn 43, Issue 3, 2002, Pages 275-295

  Meddahi, Salim ^a   Márquez, Antonio ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Exterior boundary value problem; Finite element methods; Integral equations; Spectral element methods

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; FINITE ELEMENT METHOD; GALERKIN METHODS; LINEAR EQUATIONS;

SPECTRAL ELEMENT METHODS;

POISSON DISTRIBUTION;

EID: 0036846592     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(01)00174-X     Document Type: Article

References (18)

1. Adams R. Sobolev Spaces. 1975;Academic Press, New York.
2. Atkinson K.E. A discrete Galerkin method for first kind integral equations with a logarithmic kernel. J. Integral Equations Appl. 1:1988;343-363.
3. Brezzi F., Johnson C. On the coupling of boundary integral and finite element methods. Calcolo. 16:1979;189-201.
4. Canuto C., Quarteroni A. Approximation results for orthogonal polynomials in Sobolev spaces. Math. Comp. 38:1982;67-86.
5. Ciarlet P.G. The Finite Element Method for Elliptic Problems. 1978;North-Holland, Amsterdam.
6. Costabel M. Symmetric methods for the coupling of finite elements and boundary elements. Whiteman J. Jr., The Mathematics of Finite Elements and Applications IV. 1988;Academic Press, London.
7. Costabel M., Stephan E.P. Coupling of finite and boundary element methods for an elastoplastic interface problem. SIAM J. Numer. Anal. 27:1990;1212-1226.
8. Domínguez V., Sayas F.-J. Full asymptotics of Petrov-Galerkin methods for some periodic pseudodifferential equations. Adv. Comput. Math. 14:2001;75-101.
9. 2, Numer. Math. 61:1992;171-214.
10. Gatica G.N., Hsiao G.C. Boundary-Field Equation Methods for a Class of Nonlinear Problems. Pitman Res. Notes in Math. 331:1995;Longman, Harlow.
11. Johnson C., Nédélec J.C. On the coupling of boundary integral and finite element methods. Math. Comp. 35:1980;1063-1079.
12. Kress R. Linear Integral Equations. 2nd Edition:1999;Springer, New York.
13. Meddahi S. An optimal iterative process for the Johnson-Nédélec method of coupling boundary and finite elements. SIAM J. Numer. Anal. 35:1998;1393-1415.
14. Meddahi S., Sayas F.-J. A fully discrete BEM-FEM for the exterior Stokes problem in the plane. SIAM J. Numer. Anal. 37:2000;2082-2102.
15. Meddahi S., González M., Pérez P. On a FEM-BEM formulation for an exterior quasilinear problem in the plane. SIAM J. Numer. Anal. 37:2000;1820-1837.
16. Kirsch A., Monk P. An analysis of the coupling of finite-element and Nyström methods in acoustic scattering. IMA J. Numer. Anal. 14:1994;523-544.
17. Strang G. Variational crimes in the finite element method. Aziz A., The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. 1972;Academic Press, New York.
18. Ženíšek A. Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations. 1990;Academic Press, London.